Write as a Function of p 2p^2+bp+2=0

$2 p^{2} + b p + 2 = 0$

Step 1

Move all terms not containing $b$ to the right side of the equation.

Subtract $2 p^{2}$ from both sides of the equation.

$b p + 2 = - 2 p^{2}$

Subtract $2$ from both sides of the equation.

$b p = - 2 p^{2} - 2$

Step 2

Divide each term in $b p = - 2 p^{2} - 2$ by $p$ and simplify.

Divide each term in $b p = - 2 p^{2} - 2$ by $p$ .

$\frac{b p}{p} = \frac{- 2 p^{2}}{p} + \frac{- 2}{p}$

Simplify the left side.

Cancel the common factor of $p$ .

Cancel the common factor.

$\frac{b p}{p} = \frac{- 2 p^{2}}{p} + \frac{- 2}{p}$

Divide $b$ by $1$ .

$b = \frac{- 2 p^{2}}{p} + \frac{- 2}{p}$

Simplify the right side.

Simplify each term.

Cancel the common factor of $p^{2}$ and $p$ .

Factor $p$ out of $- 2 p^{2}$ .

$b = \frac{p (- 2 p)}{p} + \frac{- 2}{p}$

Cancel the common factors.

Raise $p$ to the power of $1$ .

$b = \frac{p (- 2 p)}{p^{1}} + \frac{- 2}{p}$

Factor $p$ out of $p^{1}$ .

$b = \frac{p (- 2 p)}{p \cdot 1} + \frac{- 2}{p}$

Cancel the common factor.

$b = \frac{p (- 2 p)}{p \cdot 1} + \frac{- 2}{p}$

Rewrite the expression.

$b = \frac{- 2 p}{1} + \frac{- 2}{p}$

Divide $- 2 p$ by $1$ .

$b = - 2 p + \frac{- 2}{p}$

Move the negative in front of the fraction.

$b = - 2 p - \frac{2}{p}$

Step 3

To rewrite as a function of $p$ , write the equation so that $b$ is by itself on one side of the equal sign and an expression involving only $p$ is on the other side.

$f (p) = - 2 p - \frac{2}{p}$

Write as a Function of p 2p^2+bp+2=0

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